1) Find the exact absolute max and exact min for
f(x)=x^3-3x^2-6x+4 on the closed interval [0,3]
2) Let f be continuously differentiable function on the Reals
with the following characteristics:
- f(x) is increasing from intervals (0,2) and (4,5) and
decreasing everywhere else
- f(x) > -1 on the interval (1,3) and f(x) < -1 everywhere
else
Suppose g(x) = 2f(x) + (f(x))^2. On which interval(s) is g(x)
increasing?
Find the relative extrema, if any, classify as absolute
max/min.
a.) f(x)= x+1/x-2 on [2,4]
b.) f(x)= x^(2) -2x-3 on [-2,3]
c.) f(x)= x^(2/3) (x^2-4) on [-1,3]
Solve for x:
a.) 6^(2x) =36
b.) 2^(2x) -4 * 2^(x) +4=0
c.) 3^(x-x^2) =1/9x
Determine if the following statements are true or false. If it
is true, explain why. If it is false, provide an example.
a.) If a and b are positive numbers, then (a+b)^x=a^x+b^x
b.) If x < y, then...
Find the absolute max and min of f(x)= e^-x sin(x) on the
interval [0, 2pi]
Find the absolute max and min of f(x)= (x^2) / (x^3 +1) when x
is greater or equal to 0